Diply asked about this, so I'm just going to dive right in...
PAR: Photsynthetically Available (or Active) Radiation. All radiation with a wavelength of 400nm to 700nm.
PPFD: Photosynthetic Photon Flux Density. A way to measure PAR. It's the number of photons of light falling on a given area in a given amount of time, and its units are micromoles per meter square per second (µmol m-2 s-1).
Lux: A measure of illuminance, measured in lumens per square metre.
Now, a given light source will produce a certain amount of its output as PPFD. This amount can be related directly to illuminance by way of a multiplier, and, importantly, is constant for each source type*.
Here are the multipliers to convert illuminance in Lux to PPFD for some common light sources:
Code:
Source Multiplier
Sunlight 0.0185
Fluorescent (Grolux) 0.029
Metal Halide 0.0141
Fluorescent (865/840) 0.0135
High Pressure Sodium 0.0122
Figures provided by Apogee Instruments.
So, we can multiply the Lux value by the multiplier in the above table to find the PPFD in µmol m-2 s-1.
Worked example:
Code:
60 cm x 60 cm space (0.36 m²)
250 Watt HPS lamp (33,200 lumens)
Lux = (total lumens) / (total area in square metres)
= 33,200 / 0.36
= 92,222
PPFD = Lux x factor
= 92,222 x 0.0122
= 1,125
What level of PPFD is good? I don't know, but I imagine that, like everything in this game, "More!" is probably the answer**. The proper information is almost certainly out there though.
As a reference, direct sunlight at midday, with a Lux value of about 100,000, will provide a PPFD of around 1,850 µmol m-2 s-1.
There's also another measure of PAR, and that's YPF (Yield Photon Flux) PAR. It's weighted more to the plant response curve, and the red end of the spectrum, than PPFD and so is probably a better measure for growing purposes, but I don't have any conversion factors.
Finally, here's a table showing the PPFD for a few lamp types and sizes:

*For suitable values of 'constant'. It's mostly constant, but may vary with specific or specialist lamps.
**There probably is a maximum upper limit, and the law of diminishing returns will probably start to take effect before that limit is reached.
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